Algebra I Notes Unit Analysis Unit 00

Transcription

1 OBJECTIVE: NQ.A.1 Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. NOTE: This standard should be taught and reinforced throughout the year when applicable. BIG IDEA: Writing the units of each variable in a real-life problem helps you determine the units for the answer. This is called unit analysis and it is often used in problem solving in science. When the same units of measure occur in the numerator and the denominator of an expression, you can cancel the units. Note: It is helpful to have conversion tables available for units of time, capacity, mass, linear measure; etc. Abbreviations of units should also be included. In real world problems, the answers are usually not numbers but quantities: numbers with units, which involves measurement. In their work in measurement up through Grade 8, students primarily measure commonly used attributes such as length, area, and volume. In high school, students encounter a wider variety of units in modeling, e.g., acceleration, currency conversions, derived quantities such as person-hours and heating degree days, social science rates such as percapita income, and rates in everyday life such as points scored per game or batting averages. They also encounter novel situations in which they themselves must conceive the attributes of interest. For example, to find a good measure of overall highway safety, they might propose measures such as fatalities per year, fatalities per year per driver, or fatalities per vehicle-mile traveled. Such a conceptual process is sometimes called quantification. Quantification is important for science, as when surface area suddenly stands out as an important variable in evaporation. Quantification is also important for companies, which must conceptualize relevant attributes and create or choose suitable measures for them. PREREQUISITE SKILLS: students must have a clear understanding of rates and unit rate and proportions students must understand reciprocals students must know unit conversions in measurement VOCABULARY: conversion factor: a factor used to convert a measured quantity to a different unit of measure without changing the relative amount unit analysis or dimensional analysis: a process that uses rates to convert measurements from one unit to another Alg I Unit 00 Notes Unit Analysis r page 1 of 5 6/10/13

2 SKILLS: write expressions, equations and inequalities including the units in order to correctly label real-world problems convert given rates to equivalent forms using different units REVIEW AND EXAMPLES: Ex 1. Convert 4 ½ feet to inches. Which ratio should be used? 12 in 1 ft or 1 ft 12 in 4.5 ft 12 in 1 1 ft 54 in 54 in 1 Ex 2. A pipe is leaking at a rate of 8 fluid ounces per minute. Use unit (dimensional) analysis to find out how many gallons the pipe is leaking per hour. (A) 3,840 gal/h (B) 0.02 gal/h (C) 3.75gal/h (D) gal/h We start by listing the given leaking rate: 8 ounces/minute then multiply by conversion factors for liquid volume so we can cancel units using unit analysis. 8 fl oz 1 min 1 c 1 pt 1 qt 1 gal 8 fl oz 2 c 2 pt 4 qt 1gal 16 min The conversion factor for minutes to hours is 60 minutes = 1 hour 1 gal 60 min gal min 1hr hr Ex ft tree casts a the fence? ft shadow. At the same time, a fence casts a 2 ft shadow. How tall is (A) ft (C) 8 ft (B) 4 Set up a proportion including units. 25 ft x 6.25 ft 2 ft (D) 12 ½ fit 2 ft 25 ft x ft 2 ft 2ft 1 x 8 ft Alg I Unit 00 Notes Unit Analysis r page 2 of 5 6/10/13

3 ASSESSMENT ITEMS: 1. Sam drives his car 150 miles in 3 hours. Find the unit rate. (A) Sam drives 1 mile per 50 hours. (B) Sam drives 50 miles per hour. (C) Sam drives 30 miles per hour. (D) Sam drives 150 miles per 3 hours. 2. A model of a boat is 13.2 inches long. The scale of the model to the original is 2 inches:5 feet. How long is the boat? (A) 5 ft (B) 6.6 ft (C) 33 ft (D) 132 ft 3. A laser printer prints 135 pages in 5 minutes. How many pages does it print in 22 minutes? (A) 110 pages (B) 220 pages (C) 594 pages (D) 2970 pages 4. Kevin ran at a rate of 13 km/h. Convert his speed to meters per minute. (A) 0.2 m/min (B) 3.6 m/min (C) 217 m/min (D) 12,000 m/min 5. Molly jogged at a rate of 6 miles per hour. What was her speed in feet per second? (A) 8.8 ft/s (B) 14.7 ft/s (C) 176 ft/s (D) 528 ft/s ANS: A 6. Tonya's dachshund puppy can sprint at a speed up to 15 feet per second. What is this speed in inches per second? (A) in./s (B) in./s (C) 150 in./s (D) 180 in./s Alg I Unit 00 Notes Unit Analysis r page 3 of 5 6/10/13

4 7. A printer prints 24 pages in 3 minutes. Which unit rate is correct? (A) pages per minute (B) 8 pages per minute (C) 72 pages per hour (D) 1440 pages per hour 8. A proofreader read 195 pages in 7 hours. To the nearest hundredth, what is her reading rate in pages per minute? (A) 0.02 pages/min (B) 0.46 pages/min (C) 1.16 pages/min (D) pages/min 9. In baseball, the pitcher s mound is 60.5 feet from home plate. If a pitcher throws a baseball 90 mph, how many seconds will it take the baseball to reach home plate? (A) 0.46 sec (B) 0.67 sec (C) 1.49 sec (D) sec ANS: A 10. The strike zone or distance across home plate is 17 inches. Determine how long a baseball pitched at 90 mph is in the strike zone. (A) 0.27 sec (B) 0.19 sec (C) 0.13 sec (D) 0.01 sec 11. In the formula F I at, F and I are measured in meters per second and t is measured in seconds. In what units is a measured? (A) meters (B) seconds (C) meters per second (D) meters per second squared Alg I Unit 00 Notes Unit Analysis r page 4 of 5 6/10/13

5 12. A train travels 120 miles in one hour. What is its speed in miles per minute? ANS: 2 mi/min 13. The ratio of the sale price of a textbook to the original price is 1:3. The original price is $81. What is the sale price? ANS: $ Shayla is 5 feet tall and casts a shadow 2 feet long. At the same time, a nearby lamppost casts a shadow 8 feet long. Write and solve a proportion to find the height of the lamppost. ANS: 20 ft 15. Find the value of x in the diagram. Given: LMNP QRST 16. A boat travels 36 miles in one hour. What is its speed in miles per minute? ANS: x = 1 in. ANS: 0.6 mi/min 17. The ratio of lemon juice to water in lemonade is 1:5. If 15 cups of water are used to make a pitcher of lemonade, how many cups of lemon juice are needed? 18. Find the value of y in the diagram. Given: LMNP QRST ANS: 3 cups ANS: y = 4.8 m Alg I Unit 00 Notes Unit Analysis r page 5 of 5 6/10/13